Theory of p-adic Distributions

S. Albeverio is Professor in the Faculty of Mathematics and Natural Sciences at the University of Bonn, Germany. A. Yu. Khrennikov is Professor of Applied Mathematics and Director of the International Center for Mathematical Modeling in Physics, Engineering and Cognitive Sciences at Växjö University, Sweden. V. M. Shelkovich is Professor in the Mathematical Department at the St Petersburg State University of Architecture and Civil Engineering, Russia.

• Preface; 1. p-Adic numbers; 2. p-Adic functions; 3. p-Adic integration theory; 4. p-Adic distributions; 5. Some results from p-adic L- and L- theories; 6. The theory of associated and quasi associated homogeneous p-adic distributions; 7. p-Adic Lizorkin spaces of test functions and distributions; 8. The theory of p-adic wavelets; 9. Pseudo-differential operators on the p-adic Lizorkin spaces; 10. Pseudo-differential equations; 11. p-Adic Schrödinger-type operator with point interactions; 12. Distributional asymptotics and p-adic Tauberian theorems; 13. Asymptotics of the p-adic singular Fourier integrals; 14. Nonlinear theories of p-adic generalized functions; A. The theory of associated and quasi associated homogeneous real distributions; B. Two identities; C. Proof of a theorem on weak asymptotic expansions; D. One 'natural' way to introduce a measure on Q; References; Index.

"... constitutes a relevant contribution to the study of wavelets and multiresolution analysis, as well as to the study of linear and semilinear evolution equations via wavelets, in a p-adic setting." W.A. Zuniga Galindo, Mathematical Reviews